The Seebeck coefficient
S
is a temperature- and material-dependent property, which linearly and causally relates the temperature difference
△
T
between the “hot” and “cold” junctions of a thermoelectric power generator (TEC-PG) to the voltage difference
△
V
. This phenomenon is the Seebeck effect (SE), and can be used to convert waste heat into usable energy. This work investigates the trends of the effective voltage output
△
V(t)
and effective Seebeck coefficient
S
'
(t)
versus several hours of activity of a solid state TEC-PG device. The effective Seebeck coefficient
S
'
(t)
here is related to a device, not just to a material’s performance. The observations are pursued in an insulated compartment in various geometrical and environmental configurations. The results indicate that the SE does not substantially depend on the geometrical and environmental configurations. However, the effective Seebeck coefficient
S
'
(t)
and the produced effective
△
V(t)
are affected by the environmental configuration, once the temperature is fixed. Heat transfer calculations do not completely explain this finding. Alternative explanations are hypothesized.
Thermoelectric Heat Conduction Energy Harvesting3. Results
Figure 2. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “away” horizontal con- figuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Mean<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x109.png" xlink:type="simple"/></inline-formula>, standard deviation<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x110.png" xlink:type="simple"/></inline-formula>, and relative error <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x111.png" xlink:type="simple"/></inline-formula> of<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x112.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x112.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x113.png" xlink:type="simple"/></inline-formula>, and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x112.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x113.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x114.png" xlink:type="simple"/></inline-formula> in the “away” hori- zontal and “toward” horizontal configurations. The values displayed for the “away” horizontal configuration are evaluated in Region 2 in the 12 - 30 hour time interval, whereas those for the “toward” horizontal configuration are evaluated in Region 2 in the 10.5 - 30 hour time interval
Device Configurations
Parameter
“away” horizontal
17.8˚C
0.2˚C
0.009
28.0 mV
0.3 mV
0.010
0.011
“toward” horizontal
18.6˚C
0.2˚C
0.010
32.4 mV
0.3 mV
0.008
0.007
Figure 3. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “toward” horizontal configuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Figure 4. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “toward” vertical con- figuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Figure 5. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “toward” horizontal- black tape configuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Figure 6. Trends of (a), (b), and (c) for the solid state TEC-PG devicein the “toward” vertical- aluminum supports configuration. Regions 1 and 2 are separated by the transient accompanying the turning-on of the hot plate.
Mean<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x181.png" xlink:type="simple"/></inline-formula>, standard deviation<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x181.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x182.png" xlink:type="simple"/></inline-formula>, and relative error <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x181.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x182.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x183.png" xlink:type="simple"/></inline-formula> of<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x181.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x182.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x183.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x184.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x181.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x182.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x183.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x184.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x185.png" xlink:type="simple"/></inline-formula>, and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x181.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x182.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x183.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x184.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x185.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x186.png" xlink:type="simple"/></inline-formula> in the “toward” vertical configuration.The values are evaluated in region 2 in the 12 - 30 hour time interval
Device Configurations
Parameter
“toward” vertical
14.5˚C
0.2˚C
0.013
39.1 mV
0.2 mV
0.006
0.009
Mean<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x204.png" xlink:type="simple"/></inline-formula>, standard deviation<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x204.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x205.png" xlink:type="simple"/></inline-formula>, and relative error <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x204.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x205.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x206.png" xlink:type="simple"/></inline-formula> of<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x204.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x205.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x206.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x207.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x204.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x205.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x206.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x207.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x208.png" xlink:type="simple"/></inline-formula>, and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x204.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x205.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x206.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x207.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x208.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x209.png" xlink:type="simple"/></inline-formula> in the “toward” horizontal-black tape configuration. The values are evaluated in Region 2 in the 20 - 30 hour time interval
Device Configurations
Parameter
“toward” horizontal-black tape
16.4˚C
0.2˚C
0.010
31.8 mV
0.4 mV
0.012
0.009
Mean<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x218.png" xlink:type="simple"/></inline-formula>, standard deviation<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x218.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x219.png" xlink:type="simple"/></inline-formula>, and relative error <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x218.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x219.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x220.png" xlink:type="simple"/></inline-formula> of<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x218.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x219.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x220.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x221.png" xlink:type="simple"/></inline-formula>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x218.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x219.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x220.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x221.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x222.png" xlink:type="simple"/></inline-formula>, and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x218.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x219.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x220.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x221.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x222.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x223.png" xlink:type="simple"/></inline-formula> in the “toward” vertical-aluminum supports configuration. The values are evaluated in Region 2 in the 20 - 30 hour time interval
Device Configurations
Parameter
“toward” vertical-aluminum supports
18.9˚C
0.2˚C
0.008
52.0 mV
0.6 mV
0.011
0.013
and linear relationship existing between the effective and.
Temperature difference <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x281.png" xlink:type="simple"/></inline-formula> between the two thermocouple probes; corrected temperature difference in Region 2 between the “hot” and “cold” junction of the solid state TEC-PG device<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x281.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x282.png" xlink:type="simple"/></inline-formula>; experimental average effective voltage difference in Region 2<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x281.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x282.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x283.png" xlink:type="simple"/></inline-formula>, and corrected Seebeck coefficient in Region 2<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x281.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x282.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x283.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x284.png" xlink:type="simple"/></inline-formula>. The values are analyzed in the “away” and “toward” configurations, placing the thermocouple probes either on the “hot” or “cold” junctionsof the solid state TEC-PG device, and fixing, for the corrections, either the temperature of the thermocouple normally used on the “cold” or “hot” junctions of the solid state TEC-PG device. The former setting is named cold thermocouple, the latter the hot ther- mocouple
“away” horizontal “cold” junction fixed hot thermocouple
0.60˚C
17.2˚C
28.0 mV
−1.6
“toward” horizontal “cold” junction fixed hot thermocouple
1.40˚C
17.2˚C
32.4 mV
The values of initial offsets <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x293.png" xlink:type="simple"/></inline-formula> and<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x293.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x294.png" xlink:type="simple"/></inline-formula>, and of<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x293.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x294.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x295.png" xlink:type="simple"/></inline-formula>, the rate of increase of<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x293.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x294.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x295.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x296.png" xlink:type="simple"/></inline-formula>, and of<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x293.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x294.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x295.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x296.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x297.png" xlink:type="simple"/></inline-formula>, the rate of increase of<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x293.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x294.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x295.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x296.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x297.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x298.png" xlink:type="simple"/></inline-formula>. The corresponding goodness of fitting parameters <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x293.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x294.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x295.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x296.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x297.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x298.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x299.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x293.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x294.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x295.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x296.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x297.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x298.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x299.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x300.png" xlink:type="simple"/></inline-formula> are also reported. The parameters are obtained from the linear fitting of the experimental curves, as those illustrated in <xref ref-type="fig" rid="fig7">Figure 7</xref>, which were obtained in the 400 s time segment in Region 2 immediately following the turning-on of the hot plate
System Configurations
“away” horizontal
0.75˚C
1.14 mV
0.99217
0.98245
“toward” horizontal
0.28˚C
−0.62 mV
0.99456
0.9946
“toward” vertical
0.59˚C
−0.24 mV
0.99982
0.99419
“toward” horizontal-black tape
1.50˚C
0.52 mV
0.98371
0.9965
“toward” vertical-aluminum supports
0.71˚C
3.75 mV
0.99872
0.98003
4. Discussion
Figure 7. Linear fittings observed in the 400 s time segment in Region 2 immediately following the turning-on of the hot plate of the rise in (a) and (b) in the “away” horizontal configuration, and of the rise in (c) and (d) in the “toward” horizontal configuration.
To calculate the heat loss rate through the sample holder [16] in the steady state condition in Region 2, first the total resistance of the isolated solid state TEC-PG device depicted in Figure 8 without consi- dering the sample holders in the right corner of the figure, is calculated as follows:
In Equation (1), is the thickness of the material in the solid state TEC-PG device depicted in Figure 8, is its surface area, and its thermal conductivity. The factors 2 in the first and second term of the equation appear because there are two alumina-ceramic and two Cu plates in the solid state TEC-PG device depicted in
Figure 8. The factor in the third term of Equation (1) appears because there are 142 pillars of a Bi2Te3-
based alloy in the solid state TEC-PG devices used for this experiment. The values of the thermal conductivity and of the geometrical parameters are summarized in Table 7. The heat transfer rate across the solid state TEC-PG device is:
This quantity is 0.5 W, assuming a of (where K is degree Kelvin), as experimentally determined and previously discussed.
The second step is the calculation of the heat loss rate in Region 2 due to the different sample holders in the right corner of Figure 8. The sample holder’s (SH) resistance is:
where the factor is due to the parallel resistance determined by the sample holders in contact with the solid
state TEC-PG device. The values of the thermal conductivity and of the geometrical parameters of the wood and Al sample holders are reported in Table 7. Assuming isotropic heat diffusion, the heat loss rate across the sample holders in Figure 8 is:
where is the temperature difference across the sample holder: 2 K across Al, and 5 K across wood. The calculated values of are reported in Table 7, and are compared with the trends of the average effective values in the steady state in Region 2. It can be seen that the decreases and the average effective values also decrease, in order, from the Al to the wood sample holders, which is contradictory accord- ing to our hypothesis. In addition, with the Al sample holder, the heat loss rate (2.5 W) is larger than the
heat transfer rate across the solid state TEC-PG device (0.5 W).The lack of correlation between
the heat loss rates and the effective average values, suggests that heat transfer does not com- pletely explain the effective voltage production in the examined cases.
Figure 8. Model of the solid state TEC-PG device mounted to the sample holder used in the calculations of heat transfer rates across the solid state TEC-PG device and heat loss rates through the sample holders. Aluminum and wood are considered as ma- terials of the sample holders. The arrows indicate the direction of flow of the heat lost through the sample holders. C1 indi- cates the capacitor with air and a Cu plate as electrodes, and the alumina-ceramic plate (Al2O3) as dielectric layer. C2 indicates the capacitor with the other Cu plate, and the Al sample holder as electrodes, and the Al2O3 plate as dielectric layer.
Thermal conductivity (<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula>) and specific physical dimensions (length<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x398.png" xlink:type="simple"/></inline-formula>, width<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x398.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x399.png" xlink:type="simple"/></inline-formula>, and thickness<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x398.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x399.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x400.png" xlink:type="simple"/></inline-formula>) of the materials involved in the heat transfer rate <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x398.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x399.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x400.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x401.png" xlink:type="simple"/></inline-formula> across the solid state TEC-PG device, and heat loss rate <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x398.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x399.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x400.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x401.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x402.png" xlink:type="simple"/></inline-formula> through the sample holders. For the two different sample holder’s materials considered (Al and wood) the heat loss rate <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x398.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x399.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x400.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x401.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x402.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x403.png" xlink:type="simple"/></inline-formula> is calculated through resistance equations [<xref ref-type="bibr" rid="scirp.49395-ref16">16</xref>] . The temperature differences across the sample holders are:<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x398.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x399.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x400.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x401.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x402.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x403.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x404.png" xlink:type="simple"/></inline-formula>, and<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x398.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x399.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x400.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x401.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x402.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x403.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x404.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x405.png" xlink:type="simple"/></inline-formula>. The <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x397.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x398.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x399.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x400.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x401.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x402.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x403.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x404.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x405.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/7-4800261x406.png" xlink:type="simple"/></inline-formula> values are the average effective voltage difference in the steady state condition in region 2 for the wood and Al cases, and correspond to those in <xref ref-type="table" rid="table2">Table 2</xref> and <xref ref-type="table" rid="table4">Table 4</xref>
Material
Alumina-Ceramic (Al2O3) 98%
35.3 [17]
30.0
30.0
1.5
Cu (Pure)**
401.0 [18]
30.0
30.0
1.0
Bismuth Telluride (Bi2Te3)
1.5 [19]
0.8
0.8
4.5
Al
167.0 [18]
6.0
6.0
9.5
2.5
52.0
Wood
0.15 [*]
6.0
6.0
9.5
0.006
39.1
5. Summary and significanceAcknowledgements
This work was supported by the US Office of Naval Research (award # N000141410378), JMU 4-VA Consor- tium (2013), Thomas F. Jeffress and Kate Miller Jeffress Memorial Trust (grant # J-1053), JMU College of Sci- ence and Mathematics for the Summer 2014 Faculty Assistance Grant, the JMU Center for Materials Science, and the JMU Department of Physics and Astronomy. The authors thank Profs. K. Giovanetti, J. Zimmerman, S. Whisnant, D. Lawrence, K. Feitosa, and K. Fukumura (JMU) for fruitful discussions. Thanks to Dr. X. Hu, A. Fovargue, T. Benns, and J. Jarrell, for technical support and help in the construction of the insulated sample compartment.
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